Advertisements
Advertisements
Question
Find the area of the shaded region:
Advertisements
Solution
∵ Diameter of complete circle = 14 cm
∴ Radius = `14/2` = 7 cm ...`[∵ "Radius" = "Diameter"/2]`
So, area of complete circle = πr2 = `22/7 xx 7 xx 7` = 154 cm2
∵ Diameter of small circle = `7/4`cm
∴ Radius = `7/(4 xx 2) = 7/8`cm
∴ Area of two small circles = 2 × πr2
= `2 xx 22/7 xx 7/8 xx 7/8`
= `77/16`cm2
∴ Area of shaded region = Area of complete circle – Area of two small circles
= `154 - 77/16`
= `(154 xx 16 - 77)/16` ...[Taking LCM]
= `(2464 - 77)/16`
= `2387/16`
= `149 3/16`cm2
Hence, the area of shaded region is `149 3/16`cm2.
APPEARS IN
RELATED QUESTIONS
In the given figure, ΔABC is an equilateral triangle the length of whose side is equal to 10 cm, and ΔADC is right-angled at D and BD= 8cm. Find the area of the shaded region.
The perimeter of a rectangular plot of land is 80 m and its breadth is 16 m. Find the length and area of the plot.
In the following figure, OE = 20 cm. In sector OSFT, square OEFG is inscribed. Find the area of the shaded region.
If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?
If diameter of a circle is increased by 40%, then its area increase by
In the following figure, the area of the shaded region is
A racetrack is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. Find the width and the area of the track.
A square is inscribed in a circle of radius 7 cm. Find the area of the square.
The area (in cm2) of the circle that can be inscribed in a square of side 8 cm is ____________.
Pizza factory has come out with two kinds of pizzas. A square pizza of side 45 cm costs ₹ 150 and a circular pizza of diameter 50 cm costs ₹ 160 (see figure). Which pizza is a better deal?
